Means that the interest rate is applied to the previous year's principal and interest combined. (I'm earning interest on interest)

Compound interest is

exponential

Calculating Future Values

FV = PV x (1 + rate per period)# of periods

What if compounding occurs monthly? How many compounding periods are there?

12 compounding periods per year

The more frequent the compounding...

Each payment earns

Lump sums

An annuity is a series of equal payments, equally spaced in time:

What if I make annual payments? Instead of depositing one lump sum of $100 into my investment account I invest $100 at the end of each year. When payments occur at the end of each period the annuity is an.....

What if I make annual payments at the beginning of each year? Instead of depositing $100 at the end of each year I invest $100 at the beginning of each year

Finding PMT to achieve FVA (I intend to starting working at age 22 and retire at age 65. I want to have 2.5 million dollars in my savings account when I retire. I expect to earn 7% per year during the years I am working and saving. How much must I save each month?)

If i put 10,000 in the bank today, and earn annual interest of 4%, compounded annually how much will I have in my account in five years time?

Assume that when a mysterious aunt died 25 years ago, she left me 15,000. if i had invested the money at an annual rate of 9%, compound annually, how much would I have today?

If you earn a gross salary of $50,000 when you are 22 years old, and are awarded a 4% salary increase each year, what will be your annual gross salary when you are 70?

your credit card company charges a rate of 21%, compounded monthly, on all outstanding balances. If you use your credit card to buy a latte for $3.50, and it takes ten years until you completely pay off your credit card balance, how much did you end up spending on the latte?

Which has a higher future vale: a 1,000 deposit that earns a rate 0f 8%, compound quarterly, for a total of 6 years, or a $1,000 deposit that earns a rate of 8%, compounded monthly, for a total of 6 years?

assume you have a brand new baby today. you plan to make 18 $1,000 annual deposits in her college saving account, starting on her 1st birthday and concluding on her 18th birthday. if the account earns 9% per year, compounded annually, what will be the balance in her account after her 18th birthday?

The college board reports that average cost for one year of in-state tuition, fees, room and board at a 4-year public university is $20,770 for the 2017-2018 academic year. Assume total college cost rise at their historical inflation rate of approximately 5% per year, how much will one year of college cost 18 years from today? will your child be able to afford a four-year degree?

How much should you save each month, for all 18 years to pay for her college education? assume all 4 years of college cost the same amount and your college savings account earns 7% per year, compounded monthly.

Assume you invest $10,000 per year in an investment that earns annual returns of 6%. If you make your 1st deposit today (your 25th birthday, which is the beginning of your 25th year) and your 30th deposit on your 54th birthday, how much will you have on your 55th birthday?

if you make 10 additional deposits, how much will you have on your 65th birthday?

I want to have $2 million dollars in my savings account when I retire. I will start working at 22 and retire at 70. I hope to earn 8% on my account during the years I am working and saving. If I make 48 annual deposits, how much must each deposit be?

If i make monthly deposits for 48 years, how much must each deposit be?

Compounding review:

Discounting is the opposite of compounding

Present Value of a lump sum example: I want $10,000 in the bank five years from now to pay for a trip to Australia. How much must I deposit today if I expect to earn 12%, compounded annually?

What if we discount monthly?

Present value of an annuity example: you won the lottery and will receive 100,000 per year for the next 15 years. if the appropriate discount rate is 8% what is the prize worth today?

How about a combo deal? A company has offered to pay you 40,000 for each of the next 3 years, plus 100,000 at the end of the third year, for successfully completing a project. If the discount rate is 5%, what is the present value of the total compensation package?

Integrative example: Retirement planning

what will your salary be? assume you are 22 years old, your annual gross salary is $48,000 and you receive average annual pay raises of 3.5%. what will your salary be when you are 70? (48 years from today)

how long will you be retired?

how much will you need? I want to withdraw 250,252 from my retirement savings account each year, starting on my 71st birthday and ending on my 85th birthday (a total of 15 withdrawals). i think i can earn 6% on my retirement savings while I am retired. how much money must i have deposited by my 70th birthday to support myself during my retirement?

Assume you are now 25 and you want to have a million dollars by the time you are 65. if you can earn 6% per year, compounded annually, how much must you invest today?

Your bank pay 2% interest, compounded daily, on all savings account balances. If you want to have $10,000 in your account 10 years from now, how much must you invest today?

College costs average $20,770 for the 2017-2018 academic year. if the average annual increase in college costs has been 5% for the past three decades what was average cost for one year of college 30 years ago.

Assume you just deposited $8,500 into an account that earns interest of 6% per year, compounded annually. How many years will it take for your balance to reach 10,000?

I plan to deposit $250 into an account at the end of each month. The account earn 5% per year, compounded monthly. How many months will it take for my balance to reach $25,000?

Suppose you are earning a gross annual salary of $45,000. You would like to be earning a gross annual salary of $60,000 three years from today. In order for that to occur, what would your annual increase in salary have to be?

In 1980, a gallon of gas cost $1.08. According to AAA, the national average was $2.22 per gallon in 2016. What was the average annual inflation rate in the price of gas?

Today is your 20th birthday. You just learned that you will be receiving a small inheritance from a distant relative. You are to receive $5,000 on you 25th birthday, $15,000 on your 30th birthday, and $25,000 on your 45th birthday. Assuming a discount rate of 6%, what is your inheritance worth today?

Your grandmother offered you a choice of gifts: you could receive either $10,000 today, or $2,000 per year at the end of each of the next six years. Assuming a discount rate of 5% which gift is worth more today?

Your friend has asked you to help him launch a new company. He offered to pay you $1,000 per month, plus a $10,000 bonus if the company received venture capital funding. Assume you agree to work for the company for 3 years and the funding arrives at the end of the third year. Using a rate of 7%, compounded monthly, what is the present value of your compensation?

You are evaluating an investment. It promised to pay you 1,000 one year from today, 2,000 two years from today, and 3,000 three years from today. If you require a rate of return of 9% on the investment, what is the most you would be willing to pay for it today?

Suppose you have been offered the opportunity to invest in a start-up business. The owners have asked you to invest $15,000 today. Based on their forecasts, they expect that your investment will be worth $40,000 in 7 years. What annual rate of return does this imply?

Assume you have been asked to lend your relative $2,500. She agreed to pay you back in equal monthly installments over the course of 4 years. You plan to charge her 5% annual interest, compounded monthly. What should her monthly payment be?

Let's say your relative decided to pay you $75 per month instead of the amount calculated. How long will it take for her to pay off the loan in full.

A loan is the PV of an annuity

Loan payment example: I am buying a house that costs $187,500. I will pay 20% down and borrow the rest. The down payment is $37,500; the loan is $150,000. I qualify for a 30-year-fixed-rate mortgage at 6% compounded monthly. How much is each monthly payment?

How can I tell how much of each payment is principal and how much is interest?

Depreciation

Amortization

Depletion

Create an amortization schedule

An amortization schedule shows how

A shorter loan results in

Rates a 30- year and 15- year loan will differ because

What are points?

fixed rate loans

Variable rate loans (adjustable rate mortgages or ARM's)

How much house can you afford?

How lenders evaluate mortgage loan applications

Loan-to-value ratio

Front-end ratio

Back-end ratio

Len wants to buy a $250,000 house

He will make a down payment of $50,000

He will borrow $200,000 @ 5.5% for 30 years

His gross salary is $75,000 per year

Property taxes are $6,000 per year

Homeowner’s insurance costs $1,200 per year

His car loan, student loan & credit card payments total $1,475 per month
. Should he buy the house

Assume you are buying a $200,000 house. You will make a down payment equal to 20% of the purchase price (that is, 40,000) and will borrow the remaining $160,000. You will be using a 30-year fixed rate mortgage. You have an excellent credit rating so your lender said you qualified for a rate of 4.10%. Make a amortization schedule

let's say you decide to use a 15-year fixed rate mortgage instead of a 30-year mortgage. Your lender quoted a rate 3.16%. Create an amortization schedule. How does the second schedule differ from the one before

how much will you end up paying for the house if you use a 30-year mortgage?

how much will you end up paying for the house if you use a 15-year mortgage? what is the amount relative to the 30-year mortgage?

what are the pros and cons of using a 15-year versus a 30-year fixed rate mortgage?

A variable-rate mortgage (Adjustable Rate Mortgage or ARM) has an interest rate that rises and falles based on market rates. What are the pros and cons of using a variable-rate mortgage versus a fixed-rate mortgage? When would it make sense to use an ARM?

On the day that you finalize your home purchase you will need to pay both the down payment and assorted closing costs. What are closing costs?

What were the average closing costs on a $200,000 loan in Texas?

The number prior excludes title insurance which must also be paid at closing.

in addition to the 20% down payment lets assume you will pay the average amount of total closing costs and the title insurance fee. How much cash must you bring to the closing?

What does foreclosure mean? How is it different from returning a property to the lender?

Why might a mall owner choose to return property to the lender and/or be foreclosed upon?

What is a mortgage-backed security?

Why does the fact that the mortgage loans have been bundled into mortgage-backed securities make it more difficult to restructure (renegotiate) the mortgage loans?

If a mall closes, what is the impact on the values of the other properties near the mall? Why?

How to develop a lifetime portfolio

Determine your net worth

Determine your Net Worth

Determine your net worth

Contribute to your 401(k) plan

Traditional 401(k) plans:

Roth 401(k) plans:

Contribute to your 401(k) plan

Which mutual fund should you select?

look for the following features in each mutual fund you choose

Paying off expensive debt

Paying off expensive debt

Build up a cash reserve

Save for other goals

save for other goals

save for other goals

Recommended asset allocations

avoid being defrauded

avoid being defrauded: pyramid scheme

avoid being defrauded: ponzi scheme

avoid being defrauded

Bonds provide investors with future cash flows

Bond coupon payment example: a 5-year $1,000 par value bond bears a coupon rate of 4%. How much is each semi-annual coupon?

Bonds are subject to two rates

Bond example: on the day it is issued a 5-year 1,000 par value bears a coupon rate of 6%. if you expect a 6% rate of return, how much should you pay for the bond?

What is the whole bond worth?

Below Par bond example: on the day it was issued, a 5-year 1,000 par value bond bore a coupon rate of 6%. if the market rate for similar bonds is 7% how much should you pay for the bond?

Bond values change over time

bonds are exposed to interest rate risk (maturity risk)

What about "used" bonds? A 10-year 1,000 par value bond has 8 years remaining until maturity; it pays a semi-annual coupon of 7%. The current price of the bond is 1,150. If you buy the bond and hold it until it matures, how much will you earn?

When companies generate cash from operation, they can:

Dividends and repurchases convert information to investors

Companies rarely decrease dividend payments

Yield?

a stock's yield can be separated into two components

Growth stocks are characterized by

income stocks are characterized by

Many stock valuation models exist

Zero growth example: a share of preferred stock pays a dividend of $1 every quarter it is expected to continue doing so forever, Investors expect to earn a return of 8%. This is a special annuity called a perpetuity

constant growth example: a company paid a $2 annual dividend yesterday to each common stockholder the company is expected to grow at an annual rate of 6% forever. Stockholders expect a 16% return. This is also a special case, called a growing perpetuity

When people say "technology" stocks which companies are they talking about?

during the last couple of decades, have technology stocks been categorized as growth stocks or income stocks?

why do growth stocks typically avoid paying dividends?

why do income stocks pay dividends?

what percent of non-tech companies in the S&P 500 pay dividends to their shareholders?